Calculation of two-loop QCD corrections for hadronic single top-quark production in the t channel

TL;DR

This paper presents a complete two loop QCD analysis of hadronic $t$-channel single top production, achieving a color and spin decomposition and reducing two loop tensor integrals to master integrals. It delivers analytic results for the vertex corrections and a public C library to evaluate the challenging double box contributions, using a fixed mass ratio to simplify the reduction. These results enable more precise NNLO predictions for single top cross sections and differential distributions, aiding tests of the top quark weak couplings and CKM constraints. The methodology combines IBP based Laporta reduction, dimension shifting, and direct spinor projection, validated against known heavy quark form factors and implemented in public tools for broader use.

Abstract

In this article we discuss the calculation of single top-quark production in the t channel at two-loop order in QCD. In particular we present the decomposition of the amplitude according to its spin and colour structure and present complete results for the two-loop amplitudes in terms of master integrals. For the vertex corrections compact analytic expressions are given. The box contributions are implemented in a publicly available C program.

Figures (4)

• Figure 1: Born diagram for $t$-channel production of a single top quark.
• Figure 2: Sample diagrams for single top-quark production at two-loop order.
• Figure 3: Diagrams whose interference with the Born amplitude vanishes.
• Figure 4: Sample topologies contributing to $A_{1,LC}^{(2)}$.